Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2101 |
198 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=dg,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,h^b=h^82,f^c=fg1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2101×D83, C2×#24909031, #35434318, … |
| maximal normal subgroup of | #2101×D83, C2×#24909031, #35434318, … |
| maximal quotient of | #35309539, #35312319, #35312667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6078);